Carefully sort through peas looking for pebbles. Rinse until water runs clear and soak for 20 minutes in cold water.
Sweat leeks, onion, celery and carrots with a pinch of salt in the olive oil until onions turn translucent (about 10 min). Add wine and let sit for 5 min.
Add chicken broth, ham bone, peas, parsley and taragon.
Check for salt and pepper re-seasoning.
Simmer covered for 1 hour until peas are soft.
Remove ham bone and puree.
Shred any meat left on the bone and set aside.
Ladle soup into bowls and put some shredded ham in the middle and garnish with some parsley.